RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. J. Pure and Appl. Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sib. J. Pure and Appl. Math., 2017, Volume 17, Issue 2, Pages 21–38 (Mi vngu436)  

This article is cited in 3 scientific papers (total in 3 papers)

The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space

L. N. Krivonosov, V. A. Luk'yanov

Nizhny Novgorod State Technical University

Abstract: We define a conformally connected space with arbitrary signature of angular metric and present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of a conformally connected torsion-free space into irreducible gauge-invariant summands and prove the following new property of the Weyl tensor: all affine connections obtained from the Levi-Civita connection via the normalization transformation have the same conformal Weyl tensor. We describe all conformal torsion-free connections on hypersurfaces of a projective space and give some examples. We construct a global conformal connection on a hyperquadric of the projective space.

Keywords: conformally connected space, Weyl tensor of conformal curvature, angular metric, gauge transformations, curvature, torsion.

DOI: https://doi.org/10.17377/PAM.2017.17.203

Full text: PDF file (159 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences, 2018, 231:2, 189–205

UDC: 514.756.2
Received: 25.11.2015

Citation: L. N. Krivonosov, V. A. Luk'yanov, “The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space”, Sib. J. Pure and Appl. Math., 17:2 (2017), 21–38; J. Math. Sci., 231:2 (2018), 189–205

Citation in format AMSBIB
\Bibitem{KriLuk17}
\by L.~N.~Krivonosov, V.~A.~Luk'yanov
\paper The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space
\jour Sib. J. Pure and Appl. Math.
\yr 2017
\vol 17
\issue 2
\pages 21--38
\mathnet{http://mi.mathnet.ru/vngu436}
\crossref{https://doi.org/10.17377/PAM.2017.17.203}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 231
\issue 2
\pages 189--205
\crossref{https://doi.org/10.1007/s10958-018-3815-z}


Linking options:
  • http://mi.mathnet.ru/eng/vngu436
  • http://mi.mathnet.ru/eng/vngu/v17/i2/p21

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. N. Krivonosov, V. A. Lukyanov, “Konformnaya svyaznost so skalyarnoi kriviznoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 22–35  mathnet  crossref  elib
    2. L. N. Krivonosov, V. A. Lukyanov, “Osnovnaya teorema dlya (anti)avtodualnoi konformnoi svyaznosti bez krucheniya na chetyrekhmernom mnogoobrazii”, Izv. vuzov. Matem., 2019, no. 2, 29–38  mathnet  crossref
    3. L. N. Krivonosov, V. A. Lukyanov, “Uravneniya dualnosti na 4-mnogoobrazii konformnoi svyaznosti bez krucheniya i nekotorye ikh resheniya dlya nulevoi signatury”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:2 (2019), 207–228  mathnet  crossref  elib
  • Сибирский журнал чистой и прикладной математики
    Number of views:
    This page:75
    Full text:12
    References:8
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020